Experimentation or Memorization?

When you think about Mathematics, which of these words comes to mind?


Experimentation?
or
Memorization?


When I was a child, my parents were always so impressed at how "advanced" I was in mathematics for such a young boy. To them, it was like I had some sort of a gift. In 7th grade, however, something changed. My math teacher and many of her colleagues were convinced that I just didn't "get it." They would administer tests; I would solve the problems I was given and I would usually (almost always) come up with the right answer, but when I got the test back... it was marked WRONG! "Why?" I would ask.
"Because you are not doing it the way it was taught." she would say "You are coming up with the right answer, but you are not following the steps that we taught you. We are not convinced that you know what you are doing."
In 8th grade, when all of my friends were advancing to their first Algebra class, I was stuck in a class known as "Intro to Pre-Algebra!" INTRO to PRE Algebra?! It was there that I learned to conform, and to do the equations as they were taught. I was taught that Mathematics is a series of Memorization - not Experimentation!


But is this true? How could I have always gotten the right answer even when I didn't memorize the steps? Was I just a good guesser? What do you think?


Is math Memorization or Experimentation? Reflect back on some of your experiences with math. Did your teachers promote Experimentation or Memorization?


As you ponder this question, take a look at the discoveries THESE children have made:


http://www.mathman.biz/html/discover.html